Welcome to the forum!
I guess the first question would be, why not an airplane? I suspect you'd save enough on the cost of the aircraft and the flights themselves to pay for the additional rating pretty quickly.
If the answer is, "because I can only own one aircraft and it has to have rotors," you'll fit right in here!
Even in the newer, European-style tandem gyros, people making flights of the distance you propose are unusual. The bigger issue with the ArrowCopter will be availability. The company ceased production a few years ago, and there are very few out there.
But - There are a couple pilots on here knowledgeable about the ArrowCopter, and at least one has flown an AutoGyro MTO Sport across the US, so you've come to the right place. I've only enjoyed one brief flight as a passenger in an ArrowCopter, but I think it would be as good a candidate as any of the tandems.
A possible factor would be the life limits on certain parts. You're talking about 9-to-10 hours each way, and you'd run up the Hobbs pretty quick. But then again, if you're used to flying Robinsons, anticipating major overhaul expenses after 2000 hours is nothing new.
Good luck!